A brush-like grinding stone has been introduced (Patent Literature 1), which includes a holder that holds bundles of a plurality of linear abrasive members each formed by hardening an aggregated yarn of inorganic filaments, such as aluminum filaments, by a resin binder. When such a brush-like grinding stone is used for polishing or deburring the surface of a metallic workpiece, polishing is performed with the tips of the linear abrasive members while the brush-like grinding stone is rotating about the axial line thereof.